H. Abels and M. Röger, Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.6, pp.2403-2424, 2009.
DOI : 10.1016/j.anihpc.2009.06.002

V. Arnold, Sur la g??om??trie diff??rentielle des groupes de Lie de dimension infinie et ses applications ?? l'hydrodynamique des fluides parfaits, Annales de l???institut Fourier, vol.16, issue.1, pp.319-361, 1966.
DOI : 10.5802/aif.233

A. Bensoussan, G. Da-prato, M. C. Delfour, and S. K. Mitter, Representation and control of infinite-dimensional systems, Systems & Control : Foundations & Applications, 1992.

T. Biben and C. Misbah, Tumbling of vesicles under shear flow within an advected-field approach, Physical Review E, vol.5, issue.3, p.31908, 2003.
DOI : 10.1209/0295-5075/23/1/012

K. Thierry-biben, C. Kassner, and . Misbah, Phase-field approach to three-dimensional vesicle dynamics, Physical Review E, vol.440, issue.4, p.41921, 2005.
DOI : 10.1209/0295-5075/23/1/012

M. Boulakia, Existence of weak solutions for the motion of an elastic structure in an incompressible viscous fluid, Comptes Rendus Mathematique, vol.336, issue.12, pp.985-990, 2003.
DOI : 10.1016/S1631-073X(03)00235-8

M. Boulakia, Existence of Weak Solutions for the Three-Dimensional Motion of an Elastic Structure in an Incompressible Fluid, Journal of Mathematical Fluid Mechanics, vol.9, issue.2, pp.262-294, 2007.
DOI : 10.1007/s00021-005-0201-7

M. Boulakia, Existence of Weak Solutions for the Three-Dimensional Motion of an Elastic Structure in an Incompressible Fluid, Journal of Mathematical Fluid Mechanics, vol.9, issue.2, pp.262-294, 2007.
DOI : 10.1007/s00021-005-0201-7

M. Boulakia and A. Osses, Local null controllability of a two-dimensional fluid-structure interaction problem, ESAIM: Control, Optimisation and Calculus of Variations, vol.204, issue.1, pp.1-42, 2008.
DOI : 10.1016/j.jde.2004.02.004

URL : https://hal.archives-ouvertes.fr/inria-00542535

L. Caffarelli, R. Kohn, and L. Nirenberg, Partial regularity of suitable weak solutions of the navier-stokes equations, Communications on Pure and Applied Mathematics, vol.8, issue.6, pp.771-831, 1982.
DOI : 10.1090/trans2/065/03

G. Caginalp, An analysis of a phase field model of a free boundary, Archive for Rational Mechanics and Analysis, vol.92, issue.3, pp.205-245, 1986.
DOI : 10.1007/BF00254827

P. Constantin and C. Foias, Navier-Stokes equations. Chicago Lectures in Mathematics, 1988.

B. Desjardins and M. J. Esteban, Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid, Archive for Rational Mechanics and Analysis, vol.146, issue.1, pp.59-71, 1999.
DOI : 10.1007/s002050050136

B. Desjardins and M. J. Esteban, On Weak Solutions for Fluid???Rigid Structure Interaction: Compressible and Incompressible Models, Communications in Partial Differential Equations, vol.40, issue.1, pp.1399-1413, 2000.
DOI : 10.1007/BF01094193

R. J. Diperna and P. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, vol.307, issue.3, pp.511-547, 1989.
DOI : 10.1007/BFb0061716

S. Dolecki and D. L. Russell, A General Theory of Observation and Control, SIAM Journal on Control and Optimization, vol.15, issue.2, pp.185-220, 1977.
DOI : 10.1137/0315015

A. Doubova and E. Fernández-cara, SOME CONTROL RESULTS FOR SIMPLIFIED ONE-DIMENSIONAL MODELS OF FLUID-SOLID INTERACTION, Mathematical Models and Methods in Applied Sciences, vol.69, issue.05, pp.783-824, 2005.
DOI : 10.1081/PDE-120024530

Q. Du, M. Li, and C. Liu, Analysis of a phase field Navier- Stokes vesicle-fluid interaction model. Discrete Contin, Dyn. Syst. Ser. B, vol.8, issue.3, pp.539-556, 2007.

Q. Du, C. Liu, R. Ryham, and X. Wang, Energetic variational approaches in modeling vesicle and fluid interactions, Physica D: Nonlinear Phenomena, vol.238, issue.9-10, pp.9-10923, 2009.
DOI : 10.1016/j.physd.2009.02.015

Q. Du, C. Liu, and X. Wang, A phase field approach in the numerical study of the elastic bending energy for vesicle membranes, Journal of Computational Physics, vol.198, issue.2, pp.450-468, 2004.
DOI : 10.1016/j.jcp.2004.01.029

Q. Du, C. Liu, and X. Wang, Retrieving Topological Information for Phase Field Models, SIAM Journal on Applied Mathematics, vol.65, issue.6, pp.1913-1932, 2005.
DOI : 10.1137/040606417

G. David, J. Ebin, and . Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math, vol.92, issue.2, pp.102-163, 1970.

E. Maitre, P. Peyla, C. Misbah, and A. Raoult, Comparison between advected-field and level-set methods in the study of vesicle dynamics, Physica D: Nonlinear Phenomena, vol.241, issue.13, p.41921, 2005.
DOI : 10.1016/j.physd.2012.03.005

URL : https://hal.archives-ouvertes.fr/hal-00909424

C. Lawrence and . Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 1998.

H. O. Fattorini and D. L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension, Archive for Rational Mechanics and Analysis, vol.43, issue.4, pp.272-292, 1971.
DOI : 10.1007/BF00250466

A. V. Fursikov, O. Yu, and . Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series. Seoul National University Research Institute of Mathematics Global Analysis Research Center, vol.34, 1996.

G. P. Galdi, On the Steady Self???Propelled Motion of a Body in a Viscous Incompressible Fluid, Archive for Rational Mechanics and Analysis, vol.148, issue.1, pp.53-88, 1999.
DOI : 10.1007/s002050050156

F. Gozzi and P. Loreti, Regularity of the Minimum Time Function and Minimum Energy Problems: The Linear Case, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1195-1221, 1999.
DOI : 10.1137/S0363012996312763

M. D. Gunzburger, H. Lee, and G. A. Seregin, Global Existence of Weak Solutions for Viscous Incompressible Flows around a Moving Rigid Body in Three Dimensions, Journal of Mathematical Fluid Mechanics, vol.2, issue.3, pp.219-266, 2000.
DOI : 10.1007/PL00000954

K. Hoffmann and V. N. Starovoitov, On a motion of a solid body in a viscous fluid. Two-dimensional case, Adv. Math. Sci. Appl, vol.9, issue.2, pp.633-648, 1999.

K. Hoffmann and V. N. Starovoitov, On a motion of a solid body in a viscous fluid. Two-dimensional case, Adv. Math. Sci. Appl, vol.9, issue.2, pp.633-648, 1999.

O. Imanuvilov and T. Takahashi, Exact controllability of a fluid???rigid body system, Journal de Math??matiques Pures et Appliqu??es, vol.87, issue.4, pp.408-437, 2007.
DOI : 10.1016/j.matpur.2007.01.005

URL : https://hal.archives-ouvertes.fr/hal-00590648

O. Yu and . Imanuvilov, Remarks on exact controllability for the Navier- Stokes equations, ESAIM Control Optim. Calc. Var, vol.6, pp.39-72, 2001.

D. Jamet and C. Misbah, Towards a thermodynamically consistent picture of the phase-field model of vesicles: Local membrane incompressibility, Physical Review E, vol.155, issue.5, p.51907, 2007.
DOI : 10.1006/jcph.1999.6332

D. Jamet and C. Misbah, Thermodynamically consistent picture of the phase-field model of vesicles: Elimination of the surface tension, Physical Review E, vol.78, issue.4, p.41903, 2008.
DOI : 10.1103/PhysRevE.78.031902

D. Jamet and C. Misbah, Toward a thermodynamically consistent picture of the phase-field model of vesicles: Curvature energy, Physical Review E, vol.88, issue.3, p.31902, 2008.
DOI : 10.1103/PhysRevE.60.1724

N. V. Judakov, The solvability of the problem of the motion of a rigid body in a viscous incompressible fluid, Dinamika Splo?n. Sredy, (Vyp. 18 Dinamika Zidkost. so Svobod. Granicami), pp.249-253, 1974.

K. H. De-haas, C. Bloom, D. Van-den-ende, M. H. Duits, and J. Mellema, Deformation of giant lipid bilayer vesicles in shear flow, Physical Review E, vol.44, issue.6, pp.7132-7137, 1997.
DOI : 10.1103/PhysRevA.44.8356

C. Lartigue, M. Abkarian, and A. Viallat, Tank treading and unbinding of deformable vesicles in shear flow : Determination of the lift force, Physical Review Letters, vol.88, issue.6, 2002.

G. Lebeau and L. Robbiano, Contr??le Exact De L??quation De La Chaleur, Communications in Partial Differential Equations, vol.52, issue.1-2, pp.335-356, 1995.
DOI : 10.1016/0022-0396(87)90043-X

F. Lin, Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena, Communications on Pure and Applied Mathematics, vol.29, issue.6, pp.789-814, 1989.
DOI : 10.1002/cpa.3160420605

F. Lin and C. Liu, Nonparabolic dissipative systems modeling the flow of liquid crystals, Communications on Pure and Applied Mathematics, vol.9, issue.5, pp.501-537, 1995.
DOI : 10.1007/978-3-642-61798-0

F. Lin and C. Liu, Partial regularity of the dynamic system modeling the flow of liquid crystals, Discrete Contin. Dynam. Systems, vol.2, issue.1, pp.1-22, 1996.

J. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, 1969.

J. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, 1972.

P. Lions, Mathematical topics in fluid mechanics, of Oxford Lecture Series in Mathematics and its Applications, 1996.

L. Miller, A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups. Discrete Contin, Dyn. Syst. Ser. B, vol.14, issue.4, pp.1465-1485, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00411846

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

J. A. , S. Martín, V. Starovoitov, and M. Tucsnak, Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Ration. Mech. Anal, vol.161, issue.2, pp.113-147, 2002.

J. Saut and B. Scheurer, Unique continuation for some evolution equations, Journal of Differential Equations, vol.66, issue.1, pp.118-139, 1987.
DOI : 10.1016/0022-0396(87)90043-X

D. Serre, Chute libre d???un solide dans un fluide visqueux incompressible. existence, Japan Journal of Applied Mathematics, vol.52, issue.1, pp.99-110, 1987.
DOI : 10.1007/BF03167757

J. Simon, Compact sets in the spaceL p (O,T; B), Annali di Matematica Pura ed Applicata, vol.287, issue.1, pp.65-96, 1987.
DOI : 10.5802/aif.68

T. Takahashi, Analyse des équations modelisant le mouvement de système couplant des solides rigides et des fluides visqueux. thèse, 2002.

T. Takahashi, Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain, Adv. Differential Equations, vol.8, issue.12, pp.1499-1532, 2003.

G. Tenenbaum and M. Tucsnak, New blow-up rates for fast controls of Schr??dinger and heat equations, Journal of Differential Equations, vol.243, issue.1, pp.70-100, 2007.
DOI : 10.1016/j.jde.2007.06.019

G. Tenenbaum and M. Tucsnak, On the null-controllability of diffusion equations, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.4
DOI : 10.1112/jlms/s1-21.4.268

URL : https://hal.archives-ouvertes.fr/hal-01281331

M. Tucsnak and G. Weiss, Observation and control for operator semigroups Birkhäuser Advanced Texts : Basler Lehrbücher. [Birkhäuser Advanced Texts : Basel Textbooks], 2009.
DOI : 10.1007/978-3-7643-8994-9

URL : https://link.springer.com/content/pdf/bfm%3A978-3-7643-8994-9%2F1.pdf

J. Luis, V. , and E. Zuazua, Large time behavior for a simplified 1D model of fluid-solid interaction, Comm. Partial Differential Equations, vol.28, pp.9-101705, 2003.

J. Luis, V. , and E. Zuazua, Lack of collision in a simplified 1D model for fluid-solid interaction, Math. Models Methods Appl. Sci, vol.16, issue.5, pp.637-678, 2006.

X. Wang and Q. Du, Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches, Journal of Mathematical Biology, vol.51, issue.3, pp.347-371, 2008.
DOI : 10.1142/9789812816856

E. Zeidler, Nonlinear functional analysis and its applications. III Variational methods and optimization, 1985.